This should be pretty easy to fix. Check the oil level and the breather for any blockage.
I don.t understand what are you saying.!
How to check breather
The breather valve is essentially a one-way check valve. Remove it, clean it and see if it allows air to flow one way. It should have a soft rattle when it operates.It equalizes pressure in the differential without allowing water in.
looks like the breather is ok, as it literally spurted oil out and looks nasty black.
either its overfilled - or you are severely heating up the oil in the diff somehow, Are both wheels on it same sized?